Huffman Codes: Data Structures and Algorithms Project 2 - Prof. David J. Galles, Study Guides, Projects, Research of Data Structures and Algorithms

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Data Structures and Algorithms

CS245-2009S-P2Huffman Codes

Project 2^ David Galles

Department of Computer Science

University of San Francisco

Text Files All files are represented as binary digits – includingtext files Each character is represented by an integer code

ASCII – American Standard Code forInformation Interchange Text file is a sequence of binary digits whichrepresent the codes for each character.

ASCII Each character in ASCII is represented as 8 bits

We need 8 bits to represent all possiblecharacter combinations

(including control characters, and unprintablecharacters) Breaking up file into individual characters iseasy Finding the kth character in a file is easy

ASCII ASCII is not terribly efficient

All characters require 8 bits Frequently used characters require the samenumber of bits as infrequently used characters We could be more efficient if frequently usedcharacters required fewer than 8 bits, and lessfrequently used characters required more bits

Representing Codes as Trees Want to encode 4 only characters: a, b, c, d(instead of 256 characters)

How many bits are required for each code, ifeach code has the same length? 2 bits are required, since there are 4 possibleoptions to distinguish

Representing Codes as Trees Want to encode 4 only characters: a, b, c, d Pick the following codes:

a: 00 b: 01 c: 10 d: 11 We can represent these codes as a tree

Characters are stored at the leaves of the tree Code is represented by path to leaf

Representing Codes as Trees a: 01, b: 00, c: 11, d:

a

b^

c

d

0

1

0

0

1

1

Prefix Codes If no code is a prefix of any other code, thendecoding the file is unambiguous. If all codes are the same length, then no code willbe a prefix of any other code (trivially) We can create variable length codes, where nocode is a prefix of any other code

Prefix Codes & Trees

Any prefix code can be represented as a tree a: 0, b: 100, c: 101, d: 11

c

d

0

1 0

(^01)

1

a

b

File Length

If we use the code:

a:00, b:01, c:10, d: How many bits are required to encode a file of 20characters?

File Length

If we use the code:

a:0, b:100, c:101, d: How many bits are required to encode a file of 20characters?

File Length

If we use the code:

a:0, b:100, c:101, d: How many bits are required to encode a file of 20characters? It depends upon the number of a’s, b’s, c’s and d’sin the file

File Length

If we use the code:

a:0, b:100, c:101, d: How many bits are required to encode a file of:

11 a’s, 2 b’s, 2 c’s, and 5 d’s? 111 + 23 + 23 + 52 = 33 < 40

Decoding Files

We can use variable length keys to encode a textfile Given the encoded file, and the tree representationof the codes, it is easy to decode the file

c

d

0

(^10)

(^01)

1

a

b 0111001010011